Electric Fields and Charges in Different Scenarios
A point charge +q sits outside a solid
neutral
conducting
copper sphere of radius A.
The charge q is a distance r > A from the center,
on the right side.
What is the E-field at the center of the sphere?
(
A
s
s
u
m
e
e
q
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b
r
i
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m
s
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u
a
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i
o
n
)
.
+q
r
A) |E| = kq/r
2
, to left
B) kq/r
2
> |E| > 0, to left
C) |E| > 0, to right
D) E = 0
E)None of these
A
In the previous question, suppose the
copper sphere is charged, total charge +Q.
(We are still in static equilibrium.)
What is now the magnitude of the E-field at
the center of the sphere?
+q
r
A) |E| = kq/r
2
B) |E| = kQ/A
2
C) |E| = k(q-Q)/r
2
D) |E| = 0
E) None of these! /
it
’
s hard to compute
A
We have a large copper plate with
uniform surface charge density
Imagine the Gaussian surface drawn
below. Calculate the E-field a small
distance s
above
the conductor surface.
A) |E| =
/
0
B) |E| =
/2
0
C) |E| =
/4
0
D) |E| = (1/4
0
)(
/s
2
)
E) |E| =0
s
Consider two situations, both with very large (effectively
infinite) planes of charge, with the
same
uniform charge
per area
I. A plane of charge completely isolated in space:
II. A plane of charge on the surface of metal in equilib:
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Which situation has the
larger
electric field
above
the plane?
A) I
B) II
C) I and II have the same size E-field
A
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.
A
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e
+
q
i
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p
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d
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o
l
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w
.
W
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s
p
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e
?
(Assume Electrostatic equilibrium.)
+q
A)
Zero
B)
-q
C)
+q
D)
0 < q
outter
< +q
E)
-q < q
outer
< 0
q
outer
= ?
To think about: What about on the
inside
surface?
A point charge +Q is near a thin hollow
insulating sphere (radius L) with charge +Q
uniformly distributed on its surface.
W
h
a
t
i
s
t
r
u
e
o
f
E
(
p
o
i
n
t
A
)
a
n
d
E
(
B
)
?
A
)
E
(
A
)
=
0
,
E
(
B
)
<
>
0
B
)
E
(
A
)
<
>
0
,
E
(
B
)
=
0
C) Both nonzero D) Both 0 E) ??
+Q
spread out
A
c
u
b
i
c
a
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n
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n
-
c
o
n
d
u
c
t
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m
p
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c
h
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e
d
e
n
s
i
t
y
o
n
i
t
s
s
u
r
f
a
c
e
.
(
T
h
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a
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n
o
o
t
h
e
r
c
h
a
r
g
e
s
a
r
o
u
n
d
)
What is the field inside the box?
A
:
E
=
0
e
v
e
r
y
w
h
e
r
e
i
n
s
i
d
e
B
:
E
i
s
n
o
n
-
z
e
r
o
e
v
e
r
y
w
h
e
r
e
i
n
s
i
d
e
C
:
E
=
0
o
n
l
y
a
t
t
h
e
v
e
r
y
c
e
n
t
e
r
,
b
u
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n
o
n
-
z
e
r
o
e
l
s
e
w
h
e
r
e
i
n
s
i
d
e
.
D: Not enough info given
E-field inside a
cubical box
w
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o
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m
s
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f
a
c
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c
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a
r
g
e
.
The E-field lines
sneak out
the corners!
E field inside cubical box (sketch)
A point charge +q is near a neutral copper sphere
with a hollow interior space. In equilibrium, the
surface charge density
on the interior of the
hollow space is..
+q
= ?
A)
Zero everywhere
B)
Non-zero, but with
zero net total charge
on interior surface
C) Non-zero with non-
zero net total charge
on interior surface.
A HOLLOW copper sphere has total charge +Q.
A point charge +q sits outside at distance a.
A charge, q
’
, is in the hole, at the center.
(We are in static equilibrium.)
What is the magnitude of the E-field a distance r
from q
’
, (but, still in the
“
hole
”
region)
+q
A) |E| = kq
’
/r
2
B) |E| = k(q
’
-Q)/r
2
C) |E| = 0
D) |E| = kq/(a-r)
2
E) None of these! /
it
’
s hard to compute
+Q
+q
’
r
a
A HOLLOW copper sphere has total charge +Q.
A point charge +q sits outside.
A charge, q
’
, is in the hole, SHIFTED right a bit.
(We are in static equilibrium.)
What does the E field look like in the
“
hole
”
region?
+q
A)
Simple Coulomb
field (straight away
from q
’
, right up to
the wall)
B) Complicated/ it
’
s
hard to compute
+Q
+q
’
CORRECT ANSWER: D
Explore various scenarios involving electric fields and charges such as the E-field at the center of a conducting sphere, the effect of total charge on E-field, E-field above a charged conductor, charge distribution on the surface of a copper sphere with a hollow, field inside a charged non-conducting shell, and surface charge distribution near a point charge.
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Presentation Transcript
A point charge +q sits outside a solid neutral conducting copper sphere of radius A. The charge q is a distance r > A from the center, on the right side. What is the E-field at the center of the sphere? (Assume equilibrium situation). A) |E| = kq/r2, to left B) kq/r2 > |E| > 0, to left C) |E| > 0, to right D) E = 0 E)None of these +q r A
In the previous question, suppose the copper sphere is charged, total charge +Q. (We are still in static equilibrium.) What is now the magnitude of the E-field at the center of the sphere? A) |E| = kq/r2 B) |E| = kQ/A2 C) |E| = k(q-Q)/r2 D) |E| = 0 E) None of these! / it s hard to compute +q r A
We have a large copper plate with uniform surface charge density Imagine the Gaussian surface drawn below. Calculate the E-field a small distance s above the conductor surface. A) |E| = / 0 B) |E| = /2 0 C) |E| = /4 0 D) |E| = (1/4 0)( /s2) E) |E| =0 s
A neutral copper sphere has a spherical hollow in the center. A charge +q is placed in the center of the hollow. What is the total charge on the outside surface of the copper sphere? (Assume Electrostatic equilibrium.) qouter = ? A) Zero B) -q C) +q D) 0 < qoutter < +q E) -q < qouter < 0 +q To think about: What about on the inside surface?
A cubical non-conducting shell has a uniform positive charge density on its surface. (There are no other charges around) What is the field inside the box? + + + + + + + + + + E=? A: E=0 everywhere inside B: E is non-zero everywhere inside C: E=0 only at the very center, but non-zero elsewhere inside. D: Not enough info given + +
E field inside cubical box (sketch) E-field inside a cubical box with a uniform surface charge. The E-field lines sneak out the corners!
A point charge +q is near a neutral copper sphere with a hollow interior space. In equilibrium, the surface charge density on the interior of the hollow space is.. = ? A) Zero everywhere B) Non-zero, but with zero net total charge on interior surface C) Non-zero with non- zero net total charge on interior surface. +q
A HOLLOW copper sphere has total charge +Q. A point charge +q sits outside at distance a. A charge, q , is in the hole, at the center. (We are in static equilibrium.) What is the magnitude of the E-field a distance r from q , (but, still in the hole region) A) |E| = kq /r2 B) |E| = k(q -Q)/r2 C) |E| = 0 D) |E| = kq/(a-r)2 E) None of these! / it s hard to compute +q +q r a +Q
A HOLLOW copper sphere has total charge +Q. A point charge +q sits outside. A charge, q , is in the hole, SHIFTED right a bit. (We are in static equilibrium.) What does the E field look like in the hole region? A) Simple Coulomb field (straight away from q , right up to the wall) B) Complicated/ it s hard to compute +q +q +Q
